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<title>PMULHRSW — Packed Multiply High with Round and Scale </title></head>
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<h1>PMULHRSW — Packed Multiply High with Round and Scale</h1>
<table>
<tr>
<th>Opcode/Instruction</th>
<th>Op/En</th>
<th>64/32 bit Mode Support</th>
<th>CPUID Feature Flag</th>
<th>Description</th></tr>
<tr>
<td>
<p>0F 38 0B /r<sup>1</sup></p>
<p>PMULHRSW <em>mm1, mm2/m64</em></p></td>
<td>RM</td>
<td>V/V</td>
<td>SSSE3</td>
<td>Multiply 16-bit signed words, scale and round signed doublewords, pack high 16 bits to <em>mm1</em>.</td></tr>
<tr>
<td>
<p>66 0F 38 0B /r</p>
<p>PMULHRSW <em>xmm1, xmm2/m128</em></p></td>
<td>RM</td>
<td>V/V</td>
<td>SSSE3</td>
<td>Multiply 16-bit signed words, scale and round signed doublewords, pack high 16 bits to <em>xmm1</em>.</td></tr>
<tr>
<td>
<p>VEX.NDS.128.66.0F38.WIG 0B /r</p>
<p>VPMULHRSW <em>xmm1, xmm2, xmm3/m128</em></p></td>
<td>RVM</td>
<td>V/V</td>
<td>AVX</td>
<td>Multiply 16-bit signed words, scale and round signed doublewords, pack high 16 bits to <em>xmm1</em>.</td></tr>
<tr>
<td>
<p>VEX.NDS.256.66.0F38.WIG 0B /r</p>
<p>VPMULHRSW <em>ymm1, ymm2, ymm3/m256</em></p></td>
<td>RVM</td>
<td>V/V</td>
<td>AVX2</td>
<td>Multiply 16-bit signed words, scale and round signed doublewords, pack high 16 bits to <em>ymm1</em>.</td></tr>
<tr>
<td>
<p>EVEX.NDS.128.66.0F38.WIG 0B /r</p>
<p>VPMULHRSW xmm1 {k1}{z}, xmm2, xmm3/m128</p></td>
<td>FVM</td>
<td>V/V</td>
<td>
<p>AVX512VL</p>
<p>AVX512BW</p></td>
<td>Multiply 16-bit signed words, scale and round signed doublewords, pack high 16 bits to xmm1 under writemask k1.</td></tr>
<tr>
<td>
<p>EVEX.NDS.256.66.0F38.WIG 0B /r</p>
<p>VPMULHRSW ymm1 {k1}{z}, ymm2, ymm3/m256</p></td>
<td>FVM</td>
<td>V/V</td>
<td>
<p>AVX512VL</p>
<p>AVX512BW</p></td>
<td>Multiply 16-bit signed words, scale and round signed doublewords, pack high 16 bits to ymm1 under writemask k1.</td></tr>
<tr>
<td>
<p>EVEX.NDS.512.66.0F38.WIG 0B /r</p>
<p>VPMULHRSW zmm1 {k1}{z}, zmm2, zmm3/m512</p></td>
<td>FVM</td>
<td>V/V</td>
<td>AVX512BW</td>
<td>Multiply 16-bit signed words, scale and round signed doublewords, pack high 16 bits to zmm1 under writemask k1.</td></tr></table>
<p>NOTES:</p>
<p>1. See note in Section 2.4, “AVX and SSE Instruction Exception Specification” in the <em>Intel® 64 and IA-32 Architectures Software Developer’s Manual, Volume 2A</em> and Section 22.25.3, “Exception Conditions of Legacy SIMD Instructions Operating on MMX Registers” in the <em>Intel® 64 and IA-32 Architectures Software Developer’s Manual, Volume 3A</em>.</p>
<h3>Instruction Operand Encoding</h3>
<table>
<tr>
<td>Op/En</td>
<td>Operand 1</td>
<td>Operand 2</td>
<td>Operand 3</td>
<td>Operand 4</td></tr>
<tr>
<td>RM</td>
<td>ModRM:reg (r, w)</td>
<td>ModRM:r/m (r)</td>
<td>NA</td>
<td>NA</td></tr>
<tr>
<td>RVM</td>
<td>ModRM:reg (w)</td>
<td>VEX.vvvv (r)</td>
<td>ModRM:r/m (r)</td>
<td>NA</td></tr>
<tr>
<td>FVM</td>
<td>ModRM:reg (w)</td>
<td>EVEX.vvvv (r)</td>
<td>ModRM:r/m (r)</td>
<td>NA</td></tr></table>
<h2>Description</h2>
<p>PMULHRSW multiplies vertically each signed 16-bit integer from the destination operand (first operand) with the corresponding signed 16-bit integer of the source operand (second operand), producing intermediate, signed 32-bit integers. Each intermediate 32-bit integer is truncated to the 18 most significant bits. Rounding is always performed by adding 1 to the least significant bit of the 18-bit intermediate result. The final result is obtained by selecting the 16 bits immediately to the right of the most significant bit of each 18-bit intermediate result and packed to the destination operand.</p>
<p>When the source operand is a 128-bit memory operand, the operand must be aligned on a 16-byte boundary or a general-protection exception (#GP) will be generated.</p>
<p>In 64-bit mode and not encoded with VEX/EVEX, use the REX prefix to access XMM8-XMM15 registers.</p>
<p>Legacy SSE version 64-bit operand: Both operands can be MMX registers. The second source operand is an MMX register or a 64-bit memory location.</p>
<p>128-bit Legacy SSE version: The first source and destination operands are XMM registers. The second source operand is an XMM register or a 128-bit memory location. Bits (VLMAX-1:128) of the corresponding YMM destina-tion register remain unchanged.</p>
<p>VEX.128 encoded version: The first source and destination operands are XMM registers. The second source operand is an XMM register or a 128-bit memory location. Bits (VLMAX-1:128) of the destination YMM register are zeroed.</p>
<p>VEX.256 encoded version: The second source operand can be an YMM register or a 256-bit memory location. The first source and destination operands are YMM registers.</p>
<p>EVEX encoded versions: The first source operand is a ZMM/YMM/XMM register. The second source operand can be a ZMM/YMM/XMM register, a 512/256/128-bit memory location. The destination operand is a ZMM/YMM/XMM register conditionally updated with writemask k1.</p>
<h2>Operation</h2>
<p><strong>PMULHRSW (with 64-bit operands)</strong></p>
<pre>    temp0[31:0] = INT32 ((DEST[15:0] * SRC[15:0]) &gt;&gt;14) + 1;
    temp1[31:0] = INT32 ((DEST[31:16] * SRC[31:16]) &gt;&gt;14) + 1;
    temp2[31:0] = INT32 ((DEST[47:32] * SRC[47:32]) &gt;&gt; 14) + 1;
    temp3[31:0] = INT32 ((DEST[63:48] * SRc[63:48]) &gt;&gt; 14) + 1;
    DEST[15:0] = temp0[16:1];
    DEST[31:16] = temp1[16:1];
    DEST[47:32] = temp2[16:1];
    DEST[63:48] = temp3[16:1];</pre>
<p><strong>PMULHRSW (with 128-bit operand)</strong></p>
<pre>    temp0[31:0] = INT32 ((DEST[15:0] * SRC[15:0]) &gt;&gt;14) + 1;
    temp1[31:0] = INT32 ((DEST[31:16] * SRC[31:16]) &gt;&gt;14) + 1;
    temp2[31:0] = INT32 ((DEST[47:32] * SRC[47:32]) &gt;&gt;14) + 1;
    temp3[31:0] = INT32 ((DEST[63:48] * SRC[63:48]) &gt;&gt;14) + 1;
    temp4[31:0] = INT32 ((DEST[79:64] * SRC[79:64]) &gt;&gt;14) + 1;
    temp5[31:0] = INT32 ((DEST[95:80] * SRC[95:80]) &gt;&gt;14) + 1;
    temp6[31:0] = INT32 ((DEST[111:96] * SRC[111:96]) &gt;&gt;14) + 1;
    temp7[31:0] = INT32 ((DEST[127:112] * SRC[127:112) &gt;&gt;14) + 1;
    DEST[15:0] = temp0[16:1];
    DEST[31:16] = temp1[16:1];
    DEST[47:32] = temp2[16:1];
    DEST[63:48] = temp3[16:1];
    DEST[79:64] = temp4[16:1];
    DEST[95:80] = temp5[16:1];
    DEST[111:96] = temp6[16:1];
    DEST[127:112] = temp7[16:1];</pre>
<p><strong>VPMULHRSW (VEX.128 encoded version)</strong></p>
<pre>temp0[31:0] (cid:197) INT32 ((SRC1[15:0] * SRC2[15:0]) &gt;&gt;14) + 1
temp1[31:0] (cid:197) INT32 ((SRC1[31:16] * SRC2[31:16]) &gt;&gt;14) + 1
temp2[31:0] (cid:197) INT32 ((SRC1[47:32] * SRC2[47:32]) &gt;&gt;14) + 1
temp3[31:0] (cid:197) INT32 ((SRC1[63:48] * SRC2[63:48]) &gt;&gt;14) + 1
temp4[31:0] (cid:197) INT32 ((SRC1[79:64] * SRC2[79:64]) &gt;&gt;14) + 1
temp5[31:0] (cid:197) INT32 ((SRC1[95:80] * SRC2[95:80]) &gt;&gt;14) + 1
temp6[31:0] (cid:197) INT32 ((SRC1[111:96] * SRC2[111:96]) &gt;&gt;14) + 1
temp7[31:0] (cid:197) INT32 ((SRC1[127:112] * SRC2[127:112) &gt;&gt;14) + 1
DEST[15:0] (cid:197) temp0[16:1]
DEST[31:16] (cid:197) temp1[16:1]
DEST[47:32] (cid:197) temp2[16:1]
DEST[63:48] (cid:197) temp3[16:1]
DEST[79:64] (cid:197) temp4[16:1]
DEST[95:80] (cid:197) temp5[16:1]
DEST[111:96] (cid:197) temp6[16:1]
DEST[127:112] (cid:197) temp7[16:1]
DEST[VLMAX-1:128] (cid:197) 0</pre>
<p><strong>VPMULHRSW (VEX.256 encoded version)</strong></p>
<pre>temp0[31:0] (cid:197) INT32 ((SRC1[15:0] * SRC2[15:0]) &gt;&gt;14) + 1
temp1[31:0] (cid:197) INT32 ((SRC1[31:16] * SRC2[31:16]) &gt;&gt;14) + 1
temp2[31:0] (cid:197) INT32 ((SRC1[47:32] * SRC2[47:32]) &gt;&gt;14) + 1
temp3[31:0] (cid:197) INT32 ((SRC1[63:48] * SRC2[63:48]) &gt;&gt;14) + 1
temp4[31:0] (cid:197) INT32 ((SRC1[79:64] * SRC2[79:64]) &gt;&gt;14) + 1
temp5[31:0] (cid:197) INT32 ((SRC1[95:80] * SRC2[95:80]) &gt;&gt;14) + 1
temp6[31:0] (cid:197) INT32 ((SRC1[111:96] * SRC2[111:96]) &gt;&gt;14) + 1
temp7[31:0] (cid:197) INT32 ((SRC1[127:112] * SRC2[127:112) &gt;&gt;14) + 1
temp8[31:0] (cid:197) INT32 ((SRC1[143:128] * SRC2[143:128]) &gt;&gt;14) + 1
temp9[31:0] (cid:197) INT32 ((SRC1[159:144] * SRC2[159:144]) &gt;&gt;14) + 1
temp10[31:0] (cid:197) INT32 ((SRC1[75:160] * SRC2[175:160]) &gt;&gt;14) + 1
temp11[31:0] (cid:197) INT32 ((SRC1[191:176] * SRC2[191:176]) &gt;&gt;14) + 1
temp12[31:0] (cid:197) INT32 ((SRC1[207:192] * SRC2[207:192]) &gt;&gt;14) + 1
temp13[31:0] (cid:197) INT32 ((SRC1[223:208] * SRC2[223:208]) &gt;&gt;14) + 1
temp14[31:0] (cid:197) INT32 ((SRC1[239:224] * SRC2[239:224]) &gt;&gt;14) + 1
temp15[31:0] (cid:197) INT32 ((SRC1[255:240] * SRC2[255:240) &gt;&gt;14) + 1
DEST[15:0] (cid:197) temp0[16:1]
DEST[31:16] (cid:197) temp1[16:1]
DEST[47:32] (cid:197) temp2[16:1]
DEST[63:48] (cid:197) temp3[16:1]
DEST[79:64] (cid:197) temp4[16:1]
DEST[95:80] (cid:197) temp5[16:1]
DEST[111:96] (cid:197) temp6[16:1]
DEST[127:112] (cid:197) temp7[16:1]
DEST[143:128] (cid:197) temp8[16:1]
DEST[159:144] (cid:197) temp9[16:1]
DEST[175:160] (cid:197) temp10[16:1]
DEST[191:176] (cid:197) temp11[16:1]
DEST[207:192] (cid:197) temp12[16:1]
DEST[223:208] (cid:197) temp13[16:1]
DEST[239:224] (cid:197) temp14[16:1]
DEST[255:240] (cid:197) temp15[16:1]
DEST[MAX_VL-1:256] (cid:197) 0</pre>
<p><strong>VPMULHRSW (EVEX encoded version)</strong></p>
<pre>(KL, VL) = (8, 128), (16, 256), (32, 512)
FOR j (cid:197) 0 TO KL-1
    i (cid:197) j * 16
    IF k1[j] OR *no writemask*
         THEN
              temp[31:0] (cid:197) ((SRC1[i+15:i] * SRC2[i+15:i]) &gt;&gt;14) + 1
              DEST[i+15:i] (cid:197) tmp[16:1]
         ELSE
              IF *merging-masking*
                                                         ; merging-masking
                    THEN *DEST[i+15:i] remains unchanged*
                    ELSE *zeroing-masking*
                                                               ; zeroing-masking
                         DEST[i+15:i] (cid:197) 0
              FI
    FI;
ENDFOR
DEST[MAX_VL-1:VL] (cid:197) 0</pre>
<h2>Intel C/C++ Compiler Intrinsic Equivalents</h2>
<p>VPMULHRSW __m512i _mm512_mulhrs_epi16(__m512i a, __m512i b);</p>
<p>VPMULHRSW __m512i _mm512_mask_mulhrs_epi16(__m512i s, __mmask32 k, __m512i a, __m512i b);</p>
<p>VPMULHRSW __m512i _mm512_maskz_mulhrs_epi16( __mmask32 k, __m512i a, __m512i b);</p>
<p>VPMULHRSW __m256i _mm256_mask_mulhrs_epi16(__m256i s, __mmask16 k, __m256i a, __m256i b);</p>
<p>VPMULHRSW __m256i _mm256_maskz_mulhrs_epi16( __mmask16 k, __m256i a, __m256i b);</p>
<p>VPMULHRSW __m128i _mm_mask_mulhrs_epi16(__m128i s, __mmask8 k, __m128i a, __m128i b);</p>
<p>VPMULHRSW __m128i _mm_maskz_mulhrs_epi16( __mmask8 k, __m128i a, __m128i b);</p>
<p>PMULHRSW:</p>
<p> __m64 _mm_mulhrs_pi16 (__m64 a, __m64 b)</p>
<p>(V)PMULHRSW: __m128i _mm_mulhrs_epi16 (__m128i a, __m128i b)</p>
<p>VPMULHRSW:__m256i _mm256_mulhrs_epi16 (__m256i a, __m256i b)</p>
<h2>SIMD Floating-Point Exceptions</h2>
<p>None.</p>
<h2>Other Exceptions</h2>
<p>Non-EVEX-encoded instruction, see Exceptions Type 4.</p>
<p>EVEX-encoded instruction, see Exceptions Type E4.nb.</p></body></html>